Problem: Simplify the following expression and state the condition under which the simplification is valid: $r = \dfrac{y^2 - 5y}{y^2 + 3y - 40}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{y^2 - 5y}{y^2 + 3y - 40} = \dfrac{(y)(y - 5)}{(y + 8)(y - 5)} $ Notice that the term $(y - 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(y - 5)$ gives: $r = \dfrac{y}{y + 8}$ Since we divided by $(y - 5)$, $y \neq 5$. $r = \dfrac{y}{y + 8}; \space y \neq 5$